拟二面体群的一个无限类1-正则4度Cayley图

群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在Aut(X)中正规.得到了拟二面体群G＝〈x,y|x2m=y2=1,xy=xm 1〉(其中m=2s,s为大于4的偶数)的一个无限类4度正规1-正则Cayley图 Cay(G,S),其中S={x,x-1,xs 1y,xs-1y},并且对2r阶拟二面体群的正规1-正则4度Cayley图进行了分类,其中r＞3.证明了2r阶拟二面体群的任意4度正规1-正则Cayley图同构于Cay(G,{x,x-1,xs 1y,xs-1y}),其中s=2r-2.

An Infinite Family of One-regular and 4-valent Cayley Graphs of Quasi-dihedral Groups

A Cayley graph X=Cay(G,S) of group G is said to be normal if R(G),the group of right multiplications,is normal in Aut(X).An infinite family of normal one-regular Cayley graphs Cay(G,S) of quasi-dihedral groups G=〈x,y|x2m=y2=1,xy=xm+1〉 is obtained,where S={x,x-1,xs+1y,xs-1y},m=2s,and s is an even greater than 4.In addition,the normal and one-regular and 4-valent Cayley graphs of quasi-dihedral groups of order 2r are classified.It is proved that any 4-valent normal and one-regular Cayley graphs of quasi-dihedral ghoups G of order 2r are isomorphic to Cay(G,{x,x-1,xs+1 y,xs-1y}) where s=2r-2,r＞3.